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\left(x-6\right)\times 4+x\times 4=x\left(x-6\right)
Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,6 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(x-6\right), arā, te tauraro pātahi he tino iti rawa te kitea o x,x-6.
4x-24+x\times 4=x\left(x-6\right)
Whakamahia te āhuatanga tohatoha hei whakarea te x-6 ki te 4.
8x-24=x\left(x-6\right)
Pahekotia te 4x me x\times 4, ka 8x.
8x-24=x^{2}-6x
Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-6.
8x-24-x^{2}=-6x
Tangohia te x^{2} mai i ngā taha e rua.
8x-24-x^{2}+6x=0
Me tāpiri te 6x ki ngā taha e rua.
14x-24-x^{2}=0
Pahekotia te 8x me 6x, ka 14x.
-x^{2}+14x-24=0
Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.
a+b=14 ab=-\left(-24\right)=24
Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx-24. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
1,24 2,12 3,8 4,6
I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 24.
1+24=25 2+12=14 3+8=11 4+6=10
Tātaihia te tapeke mō ia takirua.
a=12 b=2
Ko te otinga te takirua ka hoatu i te tapeke 14.
\left(-x^{2}+12x\right)+\left(2x-24\right)
Tuhia anō te -x^{2}+14x-24 hei \left(-x^{2}+12x\right)+\left(2x-24\right).
-x\left(x-12\right)+2\left(x-12\right)
Tauwehea te -x i te tuatahi me te 2 i te rōpū tuarua.
\left(x-12\right)\left(-x+2\right)
Whakatauwehea atu te kīanga pātahi x-12 mā te whakamahi i te āhuatanga tātai tohatoha.
x=12 x=2
Hei kimi otinga whārite, me whakaoti te x-12=0 me te -x+2=0.
\left(x-6\right)\times 4+x\times 4=x\left(x-6\right)
Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,6 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(x-6\right), arā, te tauraro pātahi he tino iti rawa te kitea o x,x-6.
4x-24+x\times 4=x\left(x-6\right)
Whakamahia te āhuatanga tohatoha hei whakarea te x-6 ki te 4.
8x-24=x\left(x-6\right)
Pahekotia te 4x me x\times 4, ka 8x.
8x-24=x^{2}-6x
Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-6.
8x-24-x^{2}=-6x
Tangohia te x^{2} mai i ngā taha e rua.
8x-24-x^{2}+6x=0
Me tāpiri te 6x ki ngā taha e rua.
14x-24-x^{2}=0
Pahekotia te 8x me 6x, ka 14x.
-x^{2}+14x-24=0
Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.
x=\frac{-14±\sqrt{14^{2}-4\left(-1\right)\left(-24\right)}}{2\left(-1\right)}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 14 mō b, me -24 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-14±\sqrt{196-4\left(-1\right)\left(-24\right)}}{2\left(-1\right)}
Pūrua 14.
x=\frac{-14±\sqrt{196+4\left(-24\right)}}{2\left(-1\right)}
Whakareatia -4 ki te -1.
x=\frac{-14±\sqrt{196-96}}{2\left(-1\right)}
Whakareatia 4 ki te -24.
x=\frac{-14±\sqrt{100}}{2\left(-1\right)}
Tāpiri 196 ki te -96.
x=\frac{-14±10}{2\left(-1\right)}
Tuhia te pūtakerua o te 100.
x=\frac{-14±10}{-2}
Whakareatia 2 ki te -1.
x=-\frac{4}{-2}
Nā, me whakaoti te whārite x=\frac{-14±10}{-2} ina he tāpiri te ±. Tāpiri -14 ki te 10.
x=2
Whakawehe -4 ki te -2.
x=-\frac{24}{-2}
Nā, me whakaoti te whārite x=\frac{-14±10}{-2} ina he tango te ±. Tango 10 mai i -14.
x=12
Whakawehe -24 ki te -2.
x=2 x=12
Kua oti te whārite te whakatau.
\left(x-6\right)\times 4+x\times 4=x\left(x-6\right)
Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,6 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(x-6\right), arā, te tauraro pātahi he tino iti rawa te kitea o x,x-6.
4x-24+x\times 4=x\left(x-6\right)
Whakamahia te āhuatanga tohatoha hei whakarea te x-6 ki te 4.
8x-24=x\left(x-6\right)
Pahekotia te 4x me x\times 4, ka 8x.
8x-24=x^{2}-6x
Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-6.
8x-24-x^{2}=-6x
Tangohia te x^{2} mai i ngā taha e rua.
8x-24-x^{2}+6x=0
Me tāpiri te 6x ki ngā taha e rua.
14x-24-x^{2}=0
Pahekotia te 8x me 6x, ka 14x.
14x-x^{2}=24
Me tāpiri te 24 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.
-x^{2}+14x=24
Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.
\frac{-x^{2}+14x}{-1}=\frac{24}{-1}
Whakawehea ngā taha e rua ki te -1.
x^{2}+\frac{14}{-1}x=\frac{24}{-1}
Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.
x^{2}-14x=\frac{24}{-1}
Whakawehe 14 ki te -1.
x^{2}-14x=-24
Whakawehe 24 ki te -1.
x^{2}-14x+\left(-7\right)^{2}=-24+\left(-7\right)^{2}
Whakawehea te -14, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -7. Nā, tāpiria te pūrua o te -7 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}-14x+49=-24+49
Pūrua -7.
x^{2}-14x+49=25
Tāpiri -24 ki te 49.
\left(x-7\right)^{2}=25
Tauwehea te x^{2}-14x+49. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.
\sqrt{\left(x-7\right)^{2}}=\sqrt{25}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x-7=5 x-7=-5
Whakarūnātia.
x=12 x=2
Me tāpiri 7 ki ngā taha e rua o te whārite.